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- <title>Triangular Matrix</title>
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- <body>
- <h1><img src="../../../../boost.png" align="middle" />Triangular Matrix</h1>
- <div class="toc" id="toc"></div>
- <h2><a name="triangular_matrix"></a>Triangular Matrix</h2>
- <h4>Description</h4>
- <p>The templated class <code>triangular_matrix<T, F1, F2,
- A></code> is the base container adaptor for triangular matrices.
- For a <em>(n x n</em> )-dimensional lower triangular matrix and
- <em>0 <= i < n</em>,<em>0 <= j < n</em> holds
- <em>t</em><sub><em>i, j</em></sub> <em>= 0</em> , if <em>i >
- j</em>. If furthermore holds t<sub><em>i, i</em></sub><em>= 1</em>
- the matrix is called unit lower triangular. For a <em>(n x n</em>
- )-dimensional lower triangular matrix and <em>0 <= i <
- n</em>,<em>0 <= j < n</em> holds <em>t</em><sub><em>i,
- j</em></sub> <em>= 0</em> , if <em>i < j</em>. If furthermore
- holds t<sub><em>i, i</em></sub><em>= 1</em> the matrix is called
- unit lower triangular. The storage of triangular matrices is
- packed.</p>
- <h4>Example</h4>
- <pre>
- #include <boost/numeric/ublas/triangular.hpp>
- #include <boost/numeric/ublas/io.hpp>
- int main () {
- using namespace boost::numeric::ublas;
- triangular_matrix<double, lower> ml (3, 3);
- for (unsigned i = 0; i < ml.size1 (); ++ i)
- for (unsigned j = 0; j <= i; ++ j)
- ml (i, j) = 3 * i + j;
- std::cout << ml << std::endl;
- triangular_matrix<double, upper> mu (3, 3);
- for (unsigned i = 0; i < mu.size1 (); ++ i)
- for (unsigned j = i; j < mu.size2 (); ++ j)
- mu (i, j) = 3 * i + j;
- std::cout << mu << std::endl;
- }
- </pre>
- <p>Please read the <a href="samples/ex_triangular.cpp">full triangular example</a> for more details.</p>
- <h4>Definition</h4>
- <p>Defined in the header triangular.hpp.</p>
- <h4>Template parameters</h4>
- <table border="1" summary="parameters">
- <tbody>
- <tr>
- <th>Parameter</th>
- <th>Description</th>
- <th>Default</th>
- </tr>
- <tr>
- <td><code>T</code></td>
- <td>The type of object stored in the matrix.</td>
- <td></td>
- </tr>
- <tr>
- <td><code>F1</code></td>
- <td>Functor describing the type of the triangular matrix. <a href=
- "#triangular_matrix_1">[1]</a></td>
- <td><code>lower</code></td>
- </tr>
- <tr>
- <td><code>F2</code></td>
- <td>Functor describing the storage organization. <a href=
- "#triangular_matrix_2">[2]</a></td>
- <td><code>row_major</code></td>
- </tr>
- <tr>
- <td><code>A</code></td>
- <td>The type of the adapted array. <a href=
- "#triangular_matrix_3">[3]</a></td>
- <td><code>unbounded_array<T></code></td>
- </tr>
- </tbody>
- </table>
- <h4>Model of</h4>
- <p><a href="container_concept.html#matrix">Matrix</a> .</p>
- <h4>Type requirements</h4>
- <p>None, except for those imposed by the requirements of <a href=
- "container_concept.html#matrix">Matrix</a> .</p>
- <h4>Public base classes</h4>
- <p><code>matrix_container<triangular_matrix<T, F1, F2, A>
- ></code></p>
- <h4>Members</h4>
- <table border="1" summary="members">
- <tbody>
- <tr>
- <th>Member</th>
- <th>Description</th>
- </tr>
- <tr>
- <td><code>triangular_matrix ()</code></td>
- <td>Allocates an uninitialized <code>triangular_matrix</code> that
- holds zero rows of zero elements.</td>
- </tr>
- <tr>
- <td><code>triangular_matrix (size_type size1, size_type
- size2)</code></td>
- <td>Allocates an uninitialized <code>triangular_matrix</code> that
- holds <code>size1</code> rows of <code>size2</code> elements.</td>
- </tr>
- <tr>
- <td><code>triangular_matrix (const triangular_matrix
- &m)</code></td>
- <td>The copy constructor.</td>
- </tr>
- <tr>
- <td><code>template<class AE><br />
- triangular_matrix (const matrix_expression<AE>
- &ae)</code></td>
- <td>The extended copy constructor.</td>
- </tr>
- <tr>
- <td><code>void resize (size_type size1, size_type size2, bool
- preserve = true)</code></td>
- <td>Reallocates a <code>triangular_matrix</code> to hold
- <code>size1</code> rows of <code>size2</code> elements. The
- existing elements of the <code>triangular_matrix</code> are
- preseved when specified.</td>
- </tr>
- <tr>
- <td><code>size_type size1 () const</code></td>
- <td>Returns the number of rows.</td>
- </tr>
- <tr>
- <td><code>size_type size2 () const</code></td>
- <td>Returns the number of columns.</td>
- </tr>
- <tr>
- <td><code>const_reference operator () (size_type i, size_type j)
- const</code></td>
- <td>Returns a <code>const</code> reference of the <code>j</code>
- -th element in the <code>i</code>-th row.</td>
- </tr>
- <tr>
- <td><code>reference operator () (size_type i, size_type
- j)</code></td>
- <td>Returns a reference of the <code>j</code>-th element in the
- <code>i</code>-th row.</td>
- </tr>
- <tr>
- <td><code>triangular_matrix &operator = (const
- triangular_matrix &m)</code></td>
- <td>The assignment operator.</td>
- </tr>
- <tr>
- <td><code>triangular_matrix &assign_temporary
- (triangular_matrix &m)</code></td>
- <td>Assigns a temporary. May change the triangular matrix
- <code>m</code>.</td>
- </tr>
- <tr>
- <td><code>template<class AE><br />
- triangular_matrix &operator = (const
- matrix_expression<AE> &ae)</code></td>
- <td>The extended assignment operator.</td>
- </tr>
- <tr>
- <td><code>template<class AE><br />
- triangular_matrix &assign (const matrix_expression<AE>
- &ae)</code></td>
- <td>Assigns a matrix expression to the triangular matrix. Left and
- right hand side of the assignment should be independent.</td>
- </tr>
- <tr>
- <td><code>template<class AE><br />
- triangular_matrix &operator += (const
- matrix_expression<AE> &ae)</code></td>
- <td>A computed assignment operator. Adds the matrix expression to
- the triangular matrix.</td>
- </tr>
- <tr>
- <td><code>template<class AE><br />
- triangular_matrix &plus_assign (const
- matrix_expression<AE> &ae)</code></td>
- <td>Adds a matrix expression to the triangular matrix. Left and
- right hand side of the assignment should be independent.</td>
- </tr>
- <tr>
- <td><code>template<class AE><br />
- triangular_matrix &operator -= (const
- matrix_expression<AE> &ae)</code></td>
- <td>A computed assignment operator. Subtracts the matrix expression
- from the triangular matrix.</td>
- </tr>
- <tr>
- <td><code>template<class AE><br />
- triangular_matrix &minus_assign (const
- matrix_expression<AE> &ae)</code></td>
- <td>Subtracts a matrix expression from the triangular matrix. Left
- and right hand side of the assignment should be independent.</td>
- </tr>
- <tr>
- <td><code>template<class AT><br />
- triangular_matrix &operator *= (const AT &at)</code></td>
- <td>A computed assignment operator. Multiplies the triangular
- matrix with a scalar.</td>
- </tr>
- <tr>
- <td><code>template<class AT><br />
- triangular_matrix &operator /= (const AT &at)</code></td>
- <td>A computed assignment operator. Divides the triangular matrix
- through a scalar.</td>
- </tr>
- <tr>
- <td><code>void swap (triangular_matrix &m)</code></td>
- <td>Swaps the contents of the triangular matrices.</td>
- </tr>
- <tr>
- <td><code>void insert (size_type i, size_type j, const_reference
- t)</code></td>
- <td>Inserts the value <code>t</code> at the <code>j</code>-th
- element of the <code>i</code>-th row.</td>
- </tr>
- <tr>
- <td><code>void erase (size_type i, size_type j)</code></td>
- <td>Erases the value at the <code>j</code>-th elemenst of the
- <code>i</code>-th row.</td>
- </tr>
- <tr>
- <td><code>void clear ()</code></td>
- <td>Clears the matrix.</td>
- </tr>
- <tr>
- <td><code>const_iterator1 begin1 () const</code></td>
- <td>Returns a <code>const_iterator1</code> pointing to the
- beginning of the <code>triangular_matrix</code>.</td>
- </tr>
- <tr>
- <td><code>const_iterator1 end1 () const</code></td>
- <td>Returns a <code>const_iterator1</code> pointing to the end of
- the <code>triangular_matrix</code>.</td>
- </tr>
- <tr>
- <td><code>iterator1 begin1 ()</code></td>
- <td>Returns a <code>iterator1</code> pointing to the beginning of
- the <code>triangular_matrix</code>.</td>
- </tr>
- <tr>
- <td><code>iterator1 end1 ()</code></td>
- <td>Returns a <code>iterator1</code> pointing to the end of the
- <code>triangular_matrix</code>.</td>
- </tr>
- <tr>
- <td><code>const_iterator2 begin2 () const</code></td>
- <td>Returns a <code>const_iterator2</code> pointing to the
- beginning of the <code>triangular_matrix</code>.</td>
- </tr>
- <tr>
- <td><code>const_iterator2 end2 () const</code></td>
- <td>Returns a <code>const_iterator2</code> pointing to the end of
- the <code>triangular_matrix</code>.</td>
- </tr>
- <tr>
- <td><code>iterator2 begin2 ()</code></td>
- <td>Returns a <code>iterator2</code> pointing to the beginning of
- the <code>triangular_matrix</code>.</td>
- </tr>
- <tr>
- <td><code>iterator2 end2 ()</code></td>
- <td>Returns a <code>iterator2</code> pointing to the end of the
- <code>triangular_matrix</code>.</td>
- </tr>
- <tr>
- <td><code>const_reverse_iterator1 rbegin1 () const</code></td>
- <td>Returns a <code>const_reverse_iterator1</code> pointing to the
- beginning of the reversed <code>triangular_matrix</code>.</td>
- </tr>
- <tr>
- <td><code>const_reverse_iterator1 rend1 () const</code></td>
- <td>Returns a <code>const_reverse_iterator1</code> pointing to the
- end of the reversed <code>triangular_matrix</code>.</td>
- </tr>
- <tr>
- <td><code>reverse_iterator1 rbegin1 ()</code></td>
- <td>Returns a <code>reverse_iterator1</code> pointing to the
- beginning of the reversed <code>triangular_matrix</code>.</td>
- </tr>
- <tr>
- <td><code>reverse_iterator1 rend1 ()</code></td>
- <td>Returns a <code>reverse_iterator1</code> pointing to the end of
- the reversed <code>triangular_matrix</code>.</td>
- </tr>
- <tr>
- <td><code>const_reverse_iterator2 rbegin2 () const</code></td>
- <td>Returns a <code>const_reverse_iterator2</code> pointing to the
- beginning of the reversed <code>triangular_matrix</code>.</td>
- </tr>
- <tr>
- <td><code>const_reverse_iterator2 rend2 () const</code></td>
- <td>Returns a <code>const_reverse_iterator2</code> pointing to the
- end of the reversed <code>triangular_matrix</code>.</td>
- </tr>
- <tr>
- <td><code>reverse_iterator2 rbegin2 ()</code></td>
- <td>Returns a <code>reverse_iterator2</code> pointing to the
- beginning of the reversed <code>triangular_matrix</code>.</td>
- </tr>
- <tr>
- <td><code>reverse_iterator2 rend2 ()</code></td>
- <td>Returns a <code>reverse_iterator2</code> pointing to the end of
- the reversed <code>triangular_matrix</code>.</td>
- </tr>
- </tbody>
- </table>
- <h4>Notes</h4>
- <p><a name="triangular_matrix_1">[1]</a>
- Supported parameters for the type of the triangular matrix are
- <code>lower</code> , <code>unit_lower</code>, <code>upper</code>
- and <code>unit_upper</code> .</p>
- <p><a name="triangular_matrix_2">[2]</a>
- Supported parameters for the storage organization are
- <code>row_major</code> and <code>column_major</code>.</p>
- <p><a name="triangular_matrix_3">[3]</a>
- Supported parameters for the adapted array are
- <code>unbounded_array<T></code> ,
- <code>bounded_array<T></code> and
- <code>std::vector<T></code> .</p>
- <h2><a name="triangular_adaptor"></a>Triangular Adaptor</h2>
- <h4>Description</h4>
- <p>The templated class <code>triangular_adaptor<M, F></code>
- is a triangular matrix adaptor for other matrices.</p>
- <h4>Example</h4>
- <pre>
- #include <boost/numeric/ublas/triangular.hpp>
- #include <boost/numeric/ublas/io.hpp>
- int main () {
- using namespace boost::numeric::ublas;
- matrix<double> m (3, 3);
- triangular_adaptor<matrix<double>, lower> tal (m);
- for (unsigned i = 0; i < tal.size1 (); ++ i)
- for (unsigned j = 0; j <= i; ++ j)
- tal (i, j) = 3 * i + j;
- std::cout << tal << std::endl;
- triangular_adaptor<matrix<double>, upper> tau (m);
- for (unsigned i = 0; i < tau.size1 (); ++ i)
- for (unsigned j = i; j < tau.size2 (); ++ j)
- tau (i, j) = 3 * i + j;
- std::cout << tau << std::endl;
- }
- </pre>
- <p>Please read the <a href="samples/ex_triangular.cpp">full triangular example</a> for more details.</p>
- <h4>Definition</h4>
- <p>Defined in the header triangular.hpp.</p>
- <h4>Template parameters</h4>
- <table border="1" summary="parameters">
- <tbody>
- <tr>
- <th>Parameter</th>
- <th>Description</th>
- <th>Default</th>
- </tr>
- <tr>
- <td><code>M</code></td>
- <td>The type of the adapted matrix.</td>
- <td></td>
- </tr>
- <tr>
- <td><code>F</code></td>
- <td>Functor describing the type of the triangular adaptor. <a href=
- "#triangular_adaptor_1">[1]</a></td>
- <td><code>lower</code></td>
- </tr>
- </tbody>
- </table>
- <h4>Model of</h4>
- <p><a href="expression_concept.html#matrix_expression">Matrix Expression</a>
- .</p>
- <h4>Type requirements</h4>
- <p>None, except for those imposed by the requirements of <a href=
- "expression_concept.html#matrix_expression">Matrix Expression</a> .</p>
- <h4>Public base classes</h4>
- <p><code>matrix_expression<triangular_adaptor<M, F>
- ></code></p>
- <h4>Members</h4>
- <table border="1" summary="members">
- <tbody>
- <tr>
- <th>Member</th>
- <th>Description</th>
- </tr>
- <tr>
- <td><code>triangular_adaptor (matrix_type &data)</code></td>
- <td>Constructs a <code>triangular_adaptor</code> of a matrix.</td>
- </tr>
- <tr>
- <td><code>triangular_adaptor (const triangular_adaptor
- &m)</code></td>
- <td>The copy constructor.</td>
- </tr>
- <tr>
- <td><code>template<class AE><br />
- triangular_adaptor (const matrix_expression<AE>
- &ae)</code></td>
- <td>The extended copy constructor.</td>
- </tr>
- <tr>
- <td><code>size_type size1 () const</code></td>
- <td>Returns the number of rows.</td>
- </tr>
- <tr>
- <td><code>size_type size2 () const</code></td>
- <td>Returns the number of columns.</td>
- </tr>
- <tr>
- <td><code>const_reference operator () (size_type i, size_type j)
- const</code></td>
- <td>Returns a <code>const</code> reference of the <code>j</code>
- -th element in the <code>i</code>-th row.</td>
- </tr>
- <tr>
- <td><code>reference operator () (size_type i, size_type
- j)</code></td>
- <td>Returns a reference of the <code>j</code>-th element in the
- <code>i</code>-th row.</td>
- </tr>
- <tr>
- <td><code>triangular_adaptor &operator = (const
- triangular_adaptor &m)</code></td>
- <td>The assignment operator.</td>
- </tr>
- <tr>
- <td><code>triangular_adaptor &assign_temporary
- (triangular_adaptor &m)</code></td>
- <td>Assigns a temporary. May change the triangular adaptor
- <code>m</code>.</td>
- </tr>
- <tr>
- <td><code>template<class AE><br />
- triangular_adaptor &operator = (const
- matrix_expression<AE> &ae)</code></td>
- <td>The extended assignment operator.</td>
- </tr>
- <tr>
- <td><code>template<class AE><br />
- triangular_adaptor &assign (const matrix_expression<AE>
- &ae)</code></td>
- <td>Assigns a matrix expression to the triangular adaptor. Left and
- right hand side of the assignment should be independent.</td>
- </tr>
- <tr>
- <td><code>template<class AE><br />
- triangular_adaptor &operator += (const
- matrix_expression<AE> &ae)</code></td>
- <td>A computed assignment operator. Adds the matrix expression to
- the triangular adaptor.</td>
- </tr>
- <tr>
- <td><code>template<class AE><br />
- triangular_adaptor &plus_assign (const
- matrix_expression<AE> &ae)</code></td>
- <td>Adds a matrix expression to the triangular adaptor. Left and
- right hand side of the assignment should be independent.</td>
- </tr>
- <tr>
- <td><code>template<class AE><br />
- triangular_adaptor &operator -= (const
- matrix_expression<AE> &ae)</code></td>
- <td>A computed assignment operator. Subtracts the matrix expression
- from the triangular adaptor.</td>
- </tr>
- <tr>
- <td><code>template<class AE><br />
- triangular_adaptor &minus_assign (const
- matrix_expression<AE> &ae)</code></td>
- <td>Subtracts a matrix expression from the triangular adaptor. Left
- and right hand side of the assignment should be independent.</td>
- </tr>
- <tr>
- <td><code>template<class AT><br />
- triangular_adaptor &operator *= (const AT &at)</code></td>
- <td>A computed assignment operator. Multiplies the triangular
- adaptor with a scalar.</td>
- </tr>
- <tr>
- <td><code>template<class AT><br />
- triangular_adaptor &operator /= (const AT &at)</code></td>
- <td>A computed assignment operator. Divides the triangular adaptor
- through a scalar.</td>
- </tr>
- <tr>
- <td><code>void swap (triangular_adaptor &m)</code></td>
- <td>Swaps the contents of the triangular adaptors.</td>
- </tr>
- <tr>
- <td><code>const_iterator1 begin1 () const</code></td>
- <td>Returns a <code>const_iterator1</code> pointing to the
- beginning of the <code>triangular_adaptor</code>.</td>
- </tr>
- <tr>
- <td><code>const_iterator1 end1 () const</code></td>
- <td>Returns a <code>const_iterator1</code> pointing to the end of
- the <code>triangular_adaptor</code>.</td>
- </tr>
- <tr>
- <td><code>iterator1 begin1 ()</code></td>
- <td>Returns a <code>iterator1</code> pointing to the beginning of
- the <code>triangular_adaptor</code>.</td>
- </tr>
- <tr>
- <td><code>iterator1 end1 ()</code></td>
- <td>Returns a <code>iterator1</code> pointing to the end of the
- <code>triangular_adaptor</code>.</td>
- </tr>
- <tr>
- <td><code>const_iterator2 begin2 () const</code></td>
- <td>Returns a <code>const_iterator2</code> pointing to the
- beginning of the <code>triangular_adaptor</code>.</td>
- </tr>
- <tr>
- <td><code>const_iterator2 end2 () const</code></td>
- <td>Returns a <code>const_iterator2</code> pointing to the end of
- the <code>triangular_adaptor</code>.</td>
- </tr>
- <tr>
- <td><code>iterator2 begin2 ()</code></td>
- <td>Returns a <code>iterator2</code> pointing to the beginning of
- the <code>triangular_adaptor</code>.</td>
- </tr>
- <tr>
- <td><code>iterator2 end2 ()</code></td>
- <td>Returns a <code>iterator2</code> pointing to the end of the
- <code>triangular_adaptor</code>.</td>
- </tr>
- <tr>
- <td><code>const_reverse_iterator1 rbegin1 () const</code></td>
- <td>Returns a <code>const_reverse_iterator1</code> pointing to the
- beginning of the reversed <code>triangular_adaptor</code>.</td>
- </tr>
- <tr>
- <td><code>const_reverse_iterator1 rend1 () const</code></td>
- <td>Returns a <code>const_reverse_iterator1</code> pointing to the
- end of the reversed <code>triangular_adaptor</code>.</td>
- </tr>
- <tr>
- <td><code>reverse_iterator1 rbegin1 ()</code></td>
- <td>Returns a <code>reverse_iterator1</code> pointing to the
- beginning of the reversed <code>triangular_adaptor</code>.</td>
- </tr>
- <tr>
- <td><code>reverse_iterator1 rend1 ()</code></td>
- <td>Returns a <code>reverse_iterator1</code> pointing to the end of
- the reversed <code>triangular_adaptor</code>.</td>
- </tr>
- <tr>
- <td><code>const_reverse_iterator2 rbegin2 () const</code></td>
- <td>Returns a <code>const_reverse_iterator2</code> pointing to the
- beginning of the reversed <code>triangular_adaptor</code>.</td>
- </tr>
- <tr>
- <td><code>const_reverse_iterator2 rend2 () const</code></td>
- <td>Returns a <code>const_reverse_iterator2</code> pointing to the
- end of the reversed <code>triangular_adaptor</code>.</td>
- </tr>
- <tr>
- <td><code>reverse_iterator2 rbegin2 ()</code></td>
- <td>Returns a <code>reverse_iterator2</code> pointing to the
- beginning of the reversed <code>triangular_adaptor</code>.</td>
- </tr>
- <tr>
- <td><code>reverse_iterator2 rend2 ()</code></td>
- <td>Returns a <code>reverse_iterator2</code> pointing to the end of
- the reversed <code>triangular_adaptor</code>.</td>
- </tr>
- </tbody>
- </table>
- <h4>Notes</h4>
- <p><a name="triangular_adaptor_1">[1]</a>
- Supported parameters for the type of the triangular adaptor are
- <code>lower</code> , <code>unit_lower</code>, <code>upper</code>
- and <code>unit_upper</code> .</p>
- <hr />
- <p>Copyright (©) 2000-2002 Joerg Walter, Mathias Koch<br />
- Use, modification and distribution are subject to the
- Boost Software License, Version 1.0.
- (See accompanying file LICENSE_1_0.txt
- or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
- http://www.boost.org/LICENSE_1_0.txt
- </a>).
- </p>
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